This Problem Was Presented On MIT's 1869 Admissions Test

The Massachusetts Institute of Technology is one of the more prestigious colleges in the U.S., so it's no surprise that a math question on the admissions test is a bit tricky. Presh Talwalkar of the MindYourDecisions YouTube channel introduced the internet to one of MIT's 1869 admissions test questions. It was presented as follows: "The perpendicular dropped from the vertex of the right angle upon the hypotenuse divides it into two segments of 9 and 16 feet respectively. Find the lengths of the perpendicular, and the two legs of the triangle." What are the values of the perpendicular and the two legs? Watch the video below to see how this is solved, or scroll down to read the answer.